Statistics

Problem Statement for "TheFansAndMeetingsDivTwo"

Problem Statement

John and Brus have become very famous people all over the world, especially in Bolivia. Stories written about them by a Bolivian man have become very popular in that country. John and Brus have decided to visit their fans in Bolivia, but unfortunately, they only have time to visit one city each.

John will randomly choose one city. Each city has the same probability of being chosen. If he chooses the i-th city, he will meet between minJ[i] and maxJ[i] fans, inclusive. Each possible number of fans is equally likely. Brus will go through the exact same process, but in his case, the number of fans he would meet in the i-th city is between minB[i] and maxB[i], inclusive. Note that John and Brus are not required to visit different cities. Return the probability that John and Brus will each meet the same number of fans.

Definition

Class:
TheFansAndMeetingsDivTwo
Method:
find
Parameters:
int[], int[], int[], int[]
Returns:
double
Method signature:
double find(int[] minJ, int[] maxJ, int[] minB, int[] maxB)
(be sure your method is public)

Notes

  • The returned value must be accurate to within a relative or absolute value of 1E-9.

Constraints

  • minJ will contain between 1 and 50 elements, inclusive.
  • minJ, maxJ, minB and maxB will contain the same number of elements.
  • Each element of minJ, maxJ, minB and maxB will be between 1 and 50, inclusive.
  • The i-th element of minJ will be less than or equal to the i-th element of maxJ.
  • The i-th element of minB will be less than or equal to the i-th element of maxB.

Examples

  1. {1}

    {3}

    {1}

    {1}

    Returns: 0.3333333333333333

    Brus will definitely meet one fan, and the probability of John meeting one fan as well is 1/3.

  2. {5, 7, 7, 1, 6, 1, 1}

    {8, 9, 7, 3, 9, 5, 3}

    {9, 12, 10, 14, 50, 9, 10}

    {9, 13, 50, 15, 50, 12, 11}

    Returns: 0.014880952380952378

    The only possible same number of fans that John and Brus can meet is 9. In order for them to meet 9 fans, John must visit city 1 or city 4 and Brus must visit city 0 or city 5.

  3. {44}

    {47}

    {4}

    {7}

    Returns: 0.0

    No chance to meet the same number of fans.

  4. {1, 6, 3, 1, 4, 3, 5, 1}

    {7, 8, 5, 7, 9, 7, 9, 3}

    {5, 1, 5, 3, 1, 2, 4, 1}

    {9, 2, 7, 9, 4, 5, 4, 9}

    Returns: 0.11562305130385474

  5. {3, 1, 5, 1, 3, 1}

    {9, 5, 9, 7, 5, 10}

    {1, 1, 1, 3, 5, 5}

    {3, 1, 6, 7, 8, 5}

    Returns: 0.12251763668430339

  6. {1, 1, 7, 2, 1, 5, 1, 1}

    {3, 5, 9, 3, 9, 7, 9, 9}

    {5, 3, 6, 1, 3, 1, 7, 3}

    {6, 5, 10, 5, 4, 3, 9, 6}

    Returns: 0.11054687499999998

  7. {5, 3, 8, 1, 5, 6, 1, 4, 1}

    {9, 9, 9, 1, 7, 7, 5, 4, 3}

    {3, 1, 6, 9, 5, 3, 5, 5, 1}

    {10, 1, 10, 10, 10, 7, 8, 6, 7}

    Returns: 0.10600697068951032

  8. {10, 35, 14, 20, 18, 36, 24, 12, 10, 16, 10, 26, 39, 12, 31, 15, 14}

    {46, 37, 22, 46, 43, 42, 38, 30, 42, 30, 26, 48, 45, 28, 40, 46, 30}

    {14, 20, 16, 12, 20, 14, 33, 18, 20, 14, 26, 36, 10, 15, 30, 20, 30}

    {18, 21, 34, 48, 23, 21, 33, 30, 40, 37, 38, 46, 32, 18, 34, 22, 47}

    Returns: 0.028885315049831665

  9. {49, 22, 30, 14, 10, 24, 34, 12, 10, 46, 11, 10, 26, 10, 10, 34, 22, 10, 20, 34, 26, 30, 14, 42, 20, 15, 38, 19, 38}

    {49, 38, 40, 45, 46, 37, 39, 40, 14, 48, 32, 48, 34, 28, 18, 48, 49, 17, 35, 39, 34, 42, 33, 45, 44, 45, 48, 42, 46}

    {15, 30, 18, 30, 22, 10, 34, 15, 42, 25, 10, 23, 12, 38, 22, 32, 10, 18, 18, 36, 36, 24, 43, 26, 46, 10, 22, 28, 30}

    {32, 34, 40, 46, 42, 14, 37, 34, 44, 29, 14, 32, 40, 46, 45, 48, 38, 39, 40, 39, 45, 47, 44, 40, 48, 26, 34, 40, 42}

    Returns: 0.027465906600859916

  10. {28, 20, 38, 16, 10, 22, 35, 10, 10, 10, 16, 18, 20, 22, 42}

    {38, 28, 46, 40, 41, 46, 45, 10, 45, 10, 46, 42, 40, 46, 45}

    {34, 26, 40, 10, 25, 11, 22, 30, 40, 25, 14, 10, 42, 28, 10}

    {45, 48, 49, 14, 48, 26, 34, 32, 42, 34, 24, 10, 44, 45, 14}

    Returns: 0.03542405648787763

  11. {25, 11, 10, 14, 10, 20, 30, 26, 17, 35, 10, 18, 15, 24, 14, 32, 26, 14}

    {47, 30, 14, 30, 32, 41, 34, 45, 39, 42, 38, 43, 26, 45, 45, 48, 30, 17}

    {10, 10, 30, 10, 38, 10, 10, 12, 34, 17, 26, 31, 36, 40, 29, 10, 23, 26}

    {42, 27, 48, 45, 46, 42, 30, 32, 42, 35, 36, 46, 40, 45, 30, 38, 35, 42}

    Returns: 0.028709690556194746

  12. {10, 10, 23, 35, 10, 17, 15, 10, 19, 40, 34, 15, 34, 25, 30, 34, 10, 17}

    {10, 49, 40, 42, 37, 37, 47, 18, 30, 48, 37, 36, 45, 48, 30, 40, 45, 21}

    {14, 10, 12, 10, 14, 10, 26, 38, 13, 10, 26, 16, 10, 26, 13, 11, 14, 19}

    {30, 20, 30, 34, 14, 32, 34, 40, 22, 18, 40, 42, 38, 30, 34, 13, 26, 26}

    Returns: 0.024331436050403495

  13. {42, 10, 27, 10, 34, 42, 27, 26, 18, 12}

    {48, 46, 40, 32, 45, 45, 30, 30, 40, 45}

    {17, 18, 42, 38, 10, 26, 42, 42, 15, 30}

    {30, 40, 47, 45, 18, 46, 45, 46, 40, 38}

    Returns: 0.033826981801610735

  14. {26, 18, 10, 17, 10, 12, 15, 20, 23, 15, 38, 15, 14, 19, 41, 14, 14, 26, 10}

    {42, 42, 14, 38, 36, 42, 18, 44, 25, 45, 40, 21, 14, 42, 44, 30, 26, 26, 32}

    {32, 11, 34, 22, 16, 15, 12, 37, 10, 26, 26, 14, 34, 10, 10, 10, 26, 14, 34}

    {32, 22, 40, 32, 49, 43, 46, 38, 34, 40, 30, 30, 40, 45, 25, 27, 35, 32, 45}

    Returns: 0.028448193160877974

  15. {14, 19, 34, 34, 12, 38, 16, 16, 12, 24, 10, 10, 14, 35, 10, 40}

    {20, 46, 36, 40, 18, 44, 46, 24, 26, 42, 15, 40, 38, 45, 44, 40}

    {18, 10, 20, 24, 21, 26, 35, 10, 10, 36, 10, 10, 22, 10, 11, 40}

    {23, 22, 42, 42, 30, 32, 42, 30, 15, 38, 12, 44, 44, 30, 14, 42}

    Returns: 0.028258594005270306

  16. {26, 38, 15, 10, 25, 25, 39, 18, 12, 10, 25, 18, 14, 10, 34, 14}

    {38, 41, 26, 42, 39, 34, 45, 30, 30, 22, 30, 26, 16, 40, 37, 36}

    {25, 10, 18, 23, 10, 12, 26, 10, 20, 23, 22, 10, 12, 14, 26, 18}

    {29, 34, 26, 36, 15, 30, 28, 36, 26, 24, 32, 24, 34, 14, 36, 30}

    Returns: 0.0333697760016695

  17. {20, 38, 14, 16, 18, 19, 12, 20, 30, 30, 26, 28, 36, 10, 10, 18, 10, 25, 10, 10, 24, 10}

    {34, 46, 16, 30, 20, 45, 39, 21, 46, 48, 44, 40, 38, 46, 20, 26, 34, 30, 12, 34, 46, 35}

    {12, 38, 10, 20, 18, 10, 14, 33, 10, 28, 44, 22, 25, 10, 14, 26, 18, 26, 30, 25, 10, 30}

    {23, 46, 31, 29, 39, 18, 30, 35, 12, 30, 45, 28, 45, 26, 40, 26, 37, 43, 33, 30, 22, 42}

    Returns: 0.028165423428857656

  18. {17, 26, 18, 21, 10, 12, 10, 10, 40, 32, 18, 36, 16, 14, 15, 32, 23, 20, 15, 14}

    {32, 30, 41, 40, 29, 22, 26, 30, 45, 40, 37, 46, 26, 24, 23, 40, 35, 27, 38, 20}

    {19, 12, 10, 32, 19, 30, 18, 12, 14, 33, 10, 10, 34, 18, 10, 30, 10, 25, 34, 25}

    {30, 32, 26, 34, 42, 42, 26, 37, 26, 45, 34, 13, 39, 28, 46, 32, 14, 40, 42, 47}

    Returns: 0.02824163805763682

  19. {18, 30, 14, 26, 20, 34, 20, 15, 20, 42, 10, 18, 10, 25, 25, 13, 32, 14, 26, 34, 31, 30, 18, 13, 33, 10, 14, 20}

    {27, 46, 21, 42, 34, 40, 38, 38, 37, 46, 34, 38, 22, 34, 30, 45, 38, 42, 32, 45, 37, 42, 42, 18, 47, 20, 18, 40}

    {14, 10, 12, 38, 12, 10, 15, 12, 38, 40, 44, 22, 12, 18, 10, 10, 10, 14, 10, 37, 12, 14, 10, 10, 10, 10, 10, 10}

    {48, 31, 40, 45, 12, 26, 49, 40, 45, 45, 45, 36, 26, 26, 44, 27, 24, 15, 24, 42, 25, 35, 10, 34, 17, 45, 34, 44}

    Returns: 0.02419048357221935

  20. {10, 10, 18, 40, 26, 25, 25, 24, 18, 26}

    {44, 10, 38, 42, 34, 35, 31, 49, 37, 48}

    {10, 10, 30, 12, 28, 10, 46, 10, 40, 20}

    {12, 40, 35, 36, 30, 31, 47, 42, 45, 30}

    Returns: 0.031457656108843185

  21. {42, 45, 45, 47, 43, 40, 45, 41, 42, 43, 40, 40, 46, 44, 40, 47, 42, 40, 41, 44, 40, 47, 40, 41, 45, 45, 44}

    {49, 47, 47, 49, 49, 48, 48, 44, 48, 48, 44, 50, 47, 45, 42, 47, 50, 40, 42, 47, 47, 47, 43, 46, 49, 49, 46}

    {1, 3, 5, 7, 7, 4, 4, 1, 7, 1, 9, 1, 1, 2, 1, 7, 5, 2, 9, 3, 4, 1, 1, 1, 5, 7, 3}

    {9, 12, 7, 7, 10, 9, 4, 1, 7, 4, 9, 3, 7, 9, 1, 9, 10, 4, 9, 7, 5, 1, 12, 9, 11, 9, 4}

    Returns: 0.0

  22. {41, 44, 44, 41, 40, 41, 40, 46, 40, 40, 40, 41, 40, 40, 44, 40, 40, 45, 40, 48, 45, 41, 42, 40, 43, 41, 43, 40, 43}

    {45, 46, 45, 50, 41, 44, 50, 48, 42, 44, 41, 47, 48, 49, 49, 41, 43, 50, 41, 49, 46, 45, 49, 47, 48, 49, 43, 45, 48}

    {1, 2, 3, 1, 8, 7, 5, 1, 3, 2, 3, 7, 2, 3, 9, 1, 1, 3, 1, 5, 3, 1, 3, 3, 9, 4, 5, 5, 1}

    {1, 11, 11, 1, 9, 7, 9, 10, 5, 7, 12, 10, 7, 9, 11, 5, 5, 7, 1, 9, 3, 3, 9, 12, 10, 9, 7, 9, 12}

    Returns: 0.0

  23. {48, 43, 45, 44, 41, 40, 44, 40, 41, 44, 43, 46, 40, 40, 44, 40, 41, 40, 46, 49, 42, 41, 40, 44, 43, 40, 43, 49, 47, 40, 43, 42, 40, 40}

    {49, 49, 50, 47, 44, 44, 45, 45, 43, 47, 45, 50, 47, 43, 47, 40, 49, 46, 50, 50, 50, 49, 40, 50, 44, 47, 45, 50, 49, 50, 47, 48, 46, 40}

    {7, 1, 1, 4, 9, 5, 10, 9, 5, 9, 1, 1, 1, 5, 2, 1, 5, 1, 4, 1, 1, 1, 1, 5, 5, 10, 1, 1, 4, 2, 1, 1, 7, 4}

    {9, 1, 7, 7, 9, 12, 10, 9, 12, 9, 3, 5, 7, 10, 4, 7, 6, 3, 4, 8, 11, 10, 12, 9, 8, 11, 2, 4, 8, 10, 1, 10, 11, 9}

    Returns: 0.0

  24. {48, 40, 40, 43, 46, 43, 45, 44, 40, 45, 46, 44, 40, 42, 42, 44, 41, 40, 47, 40, 40, 45, 44, 40, 48, 46}

    {48, 43, 41, 49, 48, 44, 50, 47, 49, 49, 48, 49, 40, 49, 50, 48, 48, 49, 50, 44, 47, 49, 50, 41, 50, 48}

    {7, 5, 5, 1, 4, 1, 4, 5, 1, 7, 1, 4, 4, 1, 1, 3, 4, 1, 1, 5, 1, 1, 4, 5, 9, 4}

    {7, 8, 8, 4, 7, 4, 10, 7, 5, 10, 11, 5, 5, 10, 9, 9, 7, 10, 3, 9, 9, 7, 7, 10, 11, 12}

    Returns: 0.0

  25. {41, 41, 41, 49, 42, 40, 43, 40, 47, 40, 46, 41, 40, 42, 40, 44, 40, 40, 40, 40, 47, 42, 40}

    {47, 43, 47, 49, 43, 43, 48, 48, 47, 46, 49, 42, 41, 44, 46, 49, 45, 48, 43, 47, 48, 44, 43}

    {4, 3, 6, 1, 9, 7, 1, 1, 1, 7, 1, 1, 7, 9, 7, 3, 3, 6, 1, 7, 1, 1, 1}

    {10, 9, 8, 1, 10, 12, 9, 1, 1, 9, 3, 1, 9, 11, 11, 4, 5, 7, 7, 10, 5, 9, 11}

    Returns: 0.0

  26. {40, 41, 47, 43, 45, 43, 40, 47, 45, 42, 41, 41, 40, 45, 44, 43, 40, 40, 49, 41, 43, 45, 45, 47, 40, 41, 41, 42, 40, 42, 40, 40, 43, 40, 48, 42, 45, 43, 40, 42, 40, 41, 43, 48}

    {45, 48, 49, 49, 48, 50, 43, 50, 47, 45, 50, 47, 40, 47, 44, 47, 46, 45, 49, 50, 47, 48, 49, 48, 47, 41, 49, 45, 50, 50, 40, 41, 48, 40, 49, 50, 46, 44, 50, 43, 50, 50, 45, 49}

    {8, 5, 7, 1, 4, 1, 1, 2, 5, 1, 1, 7, 1, 4, 1, 1, 3, 9, 1, 1, 7, 1, 6, 7, 5, 1, 1, 4, 5, 1, 7, 1, 8, 1, 9, 1, 1, 1, 1, 9, 1, 1, 10, 1}

    {10, 7, 7, 7, 5, 10, 1, 10, 12, 4, 7, 9, 11, 10, 1, 1, 3, 9, 5, 5, 10, 9, 9, 8, 10, 9, 1, 6, 7, 11, 12, 7, 8, 9, 11, 5, 12, 10, 8, 12, 1, 5, 12, 7}

    Returns: 0.0

  27. {43, 49, 40, 45, 48, 40, 45, 40, 40, 41, 45, 40, 44, 47, 42, 44, 40, 42, 46, 42, 46, 45, 44, 43, 47, 43, 41, 40, 48, 40, 40, 40}

    {48, 49, 49, 47, 49, 45, 49, 40, 44, 49, 49, 44, 45, 48, 46, 46, 45, 46, 50, 45, 48, 50, 46, 45, 49, 44, 50, 40, 49, 44, 43, 44}

    {1, 1, 1, 1, 1, 7, 1, 4, 1, 1, 1, 5, 1, 1, 1, 7, 1, 4, 5, 1, 4, 5, 1, 5, 4, 2, 11, 1, 5, 5, 5, 1}

    {9, 7, 10, 9, 9, 8, 1, 4, 1, 4, 10, 7, 9, 7, 1, 12, 9, 10, 5, 1, 7, 8, 7, 9, 7, 11, 12, 7, 8, 7, 9, 1}

    Returns: 0.0

  28. {46, 40, 44, 42, 46, 47, 40, 48, 41, 41, 47, 40, 43, 48, 41, 43, 46, 40, 48, 41, 43, 46, 44, 44, 42, 41, 43, 43, 45, 46, 41, 50, 40, 48, 40, 40, 41, 44, 44, 41, 41, 40, 40, 40, 42, 40}

    {50, 46, 50, 49, 48, 50, 45, 48, 47, 42, 47, 50, 46, 50, 41, 43, 49, 48, 50, 49, 50, 48, 49, 47, 50, 44, 48, 49, 50, 50, 42, 50, 49, 49, 42, 45, 47, 44, 47, 50, 45, 42, 48, 43, 47, 42}

    {1, 1, 5, 1, 1, 1, 7, 5, 1, 1, 1, 1, 1, 1, 1, 1, 5, 3, 5, 5, 6, 4, 1, 1, 4, 11, 7, 10, 1, 5, 4, 7, 7, 1, 3, 1, 4, 1, 1, 1, 4, 1, 1, 1, 6, 1}

    {11, 6, 7, 2, 11, 4, 8, 6, 1, 1, 8, 12, 1, 7, 3, 9, 9, 7, 7, 8, 9, 9, 11, 1, 7, 11, 10, 11, 11, 12, 6, 11, 7, 7, 5, 4, 7, 7, 1, 10, 9, 5, 7, 1, 12, 10}

    Returns: 0.0

  29. {40, 40, 49, 47, 40, 41, 40, 40, 40, 45, 43, 40, 42, 40, 48, 40, 40, 43, 43, 41, 43, 42, 43, 45, 41, 42, 50}

    {41, 42, 50, 49, 42, 48, 47, 47, 48, 46, 48, 45, 48, 42, 49, 42, 46, 49, 50, 44, 45, 44, 49, 48, 41, 46, 50}

    {1, 7, 4, 1, 3, 1, 2, 1, 3, 1, 7, 6, 7, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 7, 7}

    {1, 8, 7, 11, 11, 4, 11, 9, 6, 10, 12, 10, 7, 7, 7, 11, 1, 7, 7, 3, 9, 7, 9, 4, 7, 9, 12}

    Returns: 0.0

  30. {42, 48, 50, 42, 45, 50, 43, 46, 42, 46, 40, 40, 42, 42, 48, 41, 43, 44, 40, 40, 43, 43, 40, 44, 40, 48, 42, 40}

    {44, 48, 50, 42, 46, 50, 49, 50, 45, 49, 43, 44, 49, 46, 49, 46, 47, 48, 42, 47, 45, 46, 42, 50, 41, 49, 47, 43}

    {1, 1, 1, 4, 3, 9, 10, 3, 5, 1, 1, 7, 1, 3, 4, 7, 1, 1, 1, 7, 4, 1, 3, 1, 3, 1, 3, 1}

    {9, 10, 7, 10, 4, 10, 12, 5, 7, 8, 4, 12, 10, 5, 8, 10, 9, 1, 10, 10, 11, 7, 5, 11, 7, 7, 5, 1}

    Returns: 0.0

  31. {1, 26, 15, 11, 29, 23, 19, 11, 23, 1, 37, 17, 40, 13, 22, 36, 1, 10, 23, 1, 35, 27, 5, 1, 21, 1, 43, 2, 31, 14, 29, 11, 26, 23, 1, 16, 20, 5, 17, 35, 35, 17, 16, 29, 13, 19, 6, 25, 29, 11}

    {7, 38, 23, 37, 34, 27, 35, 13, 31, 7, 41, 49, 46, 29, 31, 47, 35, 10, 49, 35, 39, 31, 13, 10, 48, 36, 47, 50, 45, 35, 31, 19, 49, 30, 1, 40, 39, 20, 43, 48, 36, 21, 19, 41, 15, 47, 41, 36, 37, 40}

    {19, 2, 7, 23, 34, 2, 34, 29, 11, 15, 17, 7, 13, 29, 15, 13, 31, 6, 13, 11, 1, 3, 35, 5, 33, 15, 26, 1, 23, 3, 17, 33, 5, 33, 8, 21, 25, 7, 1, 14, 3, 15, 6, 19, 1, 23, 19, 1, 17, 11}

    {25, 41, 45, 49, 41, 5, 44, 31, 31, 18, 49, 27, 21, 46, 41, 21, 38, 50, 31, 41, 46, 17, 48, 35, 45, 45, 29, 43, 39, 47, 21, 39, 39, 39, 19, 21, 27, 26, 5, 24, 31, 37, 47, 23, 20, 39, 29, 29, 49, 37}

    Returns: 0.022860243235238876

  32. {11, 26, 16, 1, 1, 1, 17, 3, 11, 27, 26, 9, 33, 11, 41, 1, 17, 13, 1, 33, 5, 18, 7, 17, 1, 21, 1, 9, 26, 23, 1, 21, 1, 11, 1, 11, 46, 11, 13, 11, 15, 7, 26, 16, 11, 4, 5}

    {21, 33, 47, 43, 6, 11, 45, 35, 21, 45, 49, 25, 41, 18, 49, 6, 19, 31, 11, 33, 13, 36, 37, 32, 17, 26, 30, 31, 34, 37, 31, 40, 43, 16, 25, 48, 47, 19, 40, 11, 27, 17, 41, 17, 24, 11, 26}

    {2, 7, 15, 13, 11, 26, 5, 1, 1, 3, 11, 8, 31, 11, 1, 13, 1, 1, 6, 10, 33, 31, 34, 17, 26, 16, 9, 1, 5, 9, 41, 1, 3, 35, 45, 13, 25, 1, 24, 39, 1, 33, 29, 1, 5, 1, 37}

    {49, 42, 26, 21, 33, 31, 37, 39, 3, 6, 13, 26, 32, 45, 25, 31, 32, 45, 47, 28, 36, 39, 39, 36, 45, 35, 13, 27, 48, 21, 45, 34, 41, 38, 48, 28, 29, 11, 29, 48, 26, 45, 39, 11, 25, 22, 42}

    Returns: 0.02230386821759239

  33. {20, 3, 17, 3, 19, 5, 7, 13, 17, 11, 1, 33, 3, 1, 29, 31, 3, 6, 21, 4, 6, 1, 36, 15, 3, 5, 1, 27, 17, 3, 35, 9, 27, 31, 13, 2, 7, 26, 1, 5, 29, 1, 9, 26, 21, 32, 33, 10, 31, 27}

    {47, 41, 39, 38, 21, 11, 33, 21, 27, 16, 33, 47, 19, 45, 38, 47, 3, 19, 25, 36, 26, 29, 42, 35, 50, 12, 5, 35, 17, 41, 47, 37, 31, 43, 35, 25, 47, 27, 23, 26, 31, 21, 45, 45, 31, 41, 37, 26, 45, 39}

    {19, 1, 11, 8, 6, 26, 7, 26, 13, 26, 9, 3, 3, 1, 23, 40, 14, 23, 38, 1, 7, 1, 25, 5, 1, 1, 31, 6, 35, 36, 14, 23, 5, 35, 39, 33, 27, 15, 31, 43, 26, 1, 23, 21, 15, 1, 47, 2, 36, 11}

    {31, 8, 31, 13, 26, 39, 18, 41, 19, 31, 30, 33, 22, 5, 23, 47, 46, 37, 39, 45, 21, 17, 31, 41, 36, 36, 38, 7, 43, 45, 41, 50, 21, 43, 41, 39, 33, 41, 47, 47, 33, 11, 45, 26, 35, 1, 49, 49, 47, 13}

    Returns: 0.02146575953866377

  34. {24, 1, 1, 19, 13, 11, 4, 9, 21, 3, 35, 7, 21, 13, 7, 11, 1, 19, 11, 35, 6, 11, 21, 5, 23, 16, 27, 5, 17, 8, 24, 11, 26, 23, 1, 18, 3, 29, 5, 30, 3, 31, 13, 37, 1, 11, 7, 25, 29}

    {50, 36, 36, 49, 21, 41, 26, 23, 35, 21, 45, 35, 43, 14, 19, 32, 10, 40, 49, 41, 14, 13, 39, 6, 39, 26, 41, 41, 37, 9, 27, 44, 31, 41, 23, 40, 31, 41, 41, 41, 3, 37, 21, 46, 4, 48, 41, 37, 35}

    {26, 25, 30, 21, 31, 13, 1, 5, 7, 1, 27, 19, 1, 37, 15, 7, 1, 6, 30, 2, 7, 9, 17, 1, 29, 31, 11, 39, 5, 1, 1, 15, 5, 16, 13, 27, 3, 32, 10, 13, 1, 9, 28, 33, 29, 45, 7, 10, 16}

    {36, 33, 47, 47, 37, 35, 23, 37, 45, 15, 38, 37, 15, 39, 47, 31, 9, 10, 43, 21, 21, 31, 45, 29, 47, 47, 21, 47, 31, 16, 43, 41, 7, 31, 41, 41, 42, 37, 43, 33, 47, 31, 41, 35, 46, 47, 44, 15, 29}

    Returns: 0.022892915216855023

  35. {31, 3, 21, 1, 25, 46, 19, 41, 11, 6, 25, 35, 1, 3, 41, 7, 16, 37, 3, 9, 15, 26, 3, 25, 1, 8, 32, 26, 9, 15, 28, 1, 5, 21, 41, 11, 9, 11, 25, 6, 6, 5, 28, 27, 31, 25, 5, 6}

    {37, 11, 35, 26, 33, 48, 35, 41, 42, 27, 33, 47, 40, 46, 46, 31, 31, 39, 7, 35, 16, 41, 21, 46, 47, 46, 33, 31, 41, 19, 28, 31, 15, 31, 45, 21, 9, 33, 27, 16, 42, 50, 29, 29, 46, 41, 16, 20}

    {11, 26, 1, 46, 5, 48, 9, 32, 33, 29, 21, 11, 16, 1, 23, 5, 19, 13, 6, 17, 1, 28, 43, 13, 5, 8, 6, 33, 41, 21, 11, 19, 1, 41, 3, 1, 26, 7, 1, 21, 7, 31, 31, 11, 21, 3, 21, 47}

    {13, 44, 18, 49, 11, 49, 27, 45, 43, 31, 23, 29, 19, 48, 39, 6, 45, 31, 33, 21, 24, 29, 45, 45, 45, 13, 13, 35, 44, 24, 21, 26, 1, 45, 41, 31, 41, 13, 39, 22, 8, 43, 36, 21, 38, 21, 31, 48}

    Returns: 0.02106904595221081

  36. {23, 11, 14, 1, 29, 11, 1, 16, 45, 39, 1, 8, 14, 11, 11, 3, 4, 6, 19, 13, 3, 21, 21, 19, 12, 29, 23, 24, 3, 13, 1, 17, 37, 7, 6, 37, 21, 46, 13, 37, 11, 21, 1, 15, 40, 11, 21, 21, 31}

    {47, 24, 24, 3, 35, 11, 45, 31, 46, 41, 37, 37, 37, 27, 17, 11, 30, 15, 37, 44, 33, 41, 41, 31, 39, 49, 31, 31, 40, 46, 13, 27, 41, 15, 41, 43, 49, 47, 45, 43, 43, 43, 25, 47, 49, 29, 41, 42, 34}

    {37, 25, 16, 13, 5, 7, 13, 1, 21, 16, 9, 1, 18, 26, 17, 11, 5, 16, 19, 8, 1, 11, 21, 16, 28, 21, 26, 1, 1, 20, 9, 9, 13, 28, 36, 17, 33, 18, 9, 1, 11, 46, 7, 17, 19, 11, 7, 21, 24}

    {43, 28, 46, 26, 33, 43, 41, 31, 43, 25, 13, 13, 21, 31, 30, 44, 16, 38, 23, 15, 18, 15, 37, 26, 35, 37, 37, 21, 1, 21, 41, 21, 31, 45, 41, 39, 37, 21, 30, 41, 17, 47, 27, 36, 41, 49, 38, 27, 30}

    Returns: 0.02332385489469141

  37. {21, 16, 19, 1, 21, 32, 11, 15, 15, 41, 14, 15, 39, 15, 11, 13, 1, 1, 1, 7, 31, 1, 1, 11, 1, 15, 6, 1, 25, 35, 26, 11, 19, 25, 16, 14, 31, 3, 20, 36, 5, 17, 11, 43, 9, 5, 21, 32, 10}

    {29, 41, 26, 17, 49, 35, 31, 26, 17, 43, 20, 40, 46, 33, 12, 49, 3, 21, 22, 25, 45, 39, 35, 27, 27, 34, 13, 7, 26, 43, 45, 45, 47, 38, 41, 43, 43, 6, 31, 45, 49, 25, 43, 44, 17, 15, 21, 34, 33}

    {21, 1, 14, 31, 31, 7, 8, 7, 12, 23, 3, 25, 15, 13, 31, 2, 18, 10, 1, 5, 25, 1, 21, 1, 11, 16, 7, 25, 35, 39, 1, 10, 14, 39, 1, 27, 37, 1, 11, 11, 23, 1, 7, 9, 35, 14, 5, 11, 11}

    {50, 24, 28, 41, 31, 49, 21, 27, 20, 47, 26, 25, 25, 31, 47, 31, 43, 27, 6, 11, 26, 22, 35, 41, 27, 39, 41, 41, 47, 49, 25, 13, 25, 46, 14, 47, 41, 16, 19, 17, 27, 33, 35, 31, 43, 45, 21, 17, 19}

    Returns: 0.023256816036431645

  38. {2, 1, 1, 4, 5, 11, 18, 25, 24, 15, 47, 5, 32, 31, 1, 12, 35, 5, 23, 1, 13, 5, 11, 16, 16, 1, 15, 15, 41, 33, 29, 31, 7, 14, 17, 15, 11, 9, 9, 3, 15, 30, 1, 2, 4, 6, 33}

    {13, 47, 17, 43, 21, 17, 25, 27, 25, 27, 49, 25, 41, 33, 1, 30, 44, 23, 37, 13, 46, 44, 28, 33, 28, 31, 31, 22, 45, 35, 49, 35, 28, 29, 50, 46, 41, 11, 29, 36, 15, 31, 5, 45, 41, 41, 41}

    {7, 3, 3, 27, 9, 9, 23, 6, 15, 31, 22, 21, 15, 7, 1, 21, 5, 48, 2, 39, 8, 12, 11, 31, 1, 7, 43, 1, 39, 20, 1, 14, 1, 6, 11, 5, 25, 5, 16, 15, 41, 1, 1, 20, 1, 11, 3}

    {41, 40, 8, 31, 21, 35, 41, 31, 21, 40, 31, 42, 43, 39, 5, 47, 11, 49, 31, 44, 35, 21, 28, 38, 31, 29, 44, 25, 41, 39, 20, 19, 29, 45, 39, 15, 43, 11, 44, 23, 42, 31, 46, 45, 31, 26, 36}

    Returns: 0.0223855456367634

  39. {48, 8, 1, 11, 3, 25, 16, 16, 38, 1, 39, 11, 14, 17, 14, 9, 5, 1, 25, 26, 29, 1, 1, 36, 11, 32, 1, 20, 45, 20, 3, 19, 41, 7, 14, 13, 33, 7, 7, 23, 19, 21, 5, 21, 31, 23, 3}

    {49, 33, 17, 31, 28, 31, 45, 21, 46, 21, 43, 11, 36, 31, 27, 41, 31, 32, 41, 27, 35, 27, 13, 47, 26, 33, 30, 27, 49, 27, 42, 29, 43, 37, 19, 23, 47, 12, 21, 27, 27, 27, 37, 24, 47, 46, 47}

    {1, 9, 39, 13, 5, 5, 15, 19, 11, 6, 21, 25, 13, 7, 33, 10, 1, 26, 31, 27, 1, 3, 26, 30, 1, 2, 1, 43, 31, 7, 19, 25, 17, 33, 11, 13, 27, 13, 11, 43, 11, 7, 35, 1, 31, 21, 23}

    {39, 26, 40, 18, 34, 7, 24, 26, 21, 43, 33, 50, 37, 23, 47, 31, 19, 36, 39, 45, 43, 22, 37, 43, 41, 50, 45, 47, 45, 33, 34, 37, 26, 36, 12, 40, 50, 46, 33, 46, 43, 29, 39, 43, 43, 46, 36}

    Returns: 0.022482923364524784

  40. {13, 1, 21, 2, 26, 17, 14, 14, 5, 1, 1, 1, 11, 7, 1, 13, 3, 1, 9, 9, 27, 1, 21, 1, 3, 11, 26, 3, 5, 30, 1, 21, 1, 21, 13, 19, 15, 1, 13, 1, 9, 20, 7, 39, 18, 23, 33}

    {20, 45, 32, 6, 49, 49, 21, 28, 27, 21, 12, 7, 30, 9, 22, 45, 28, 46, 50, 9, 41, 3, 44, 41, 5, 17, 47, 20, 29, 39, 9, 31, 23, 29, 47, 31, 25, 45, 49, 31, 21, 26, 35, 47, 47, 41, 44}

    {1, 39, 21, 3, 7, 7, 11, 5, 41, 24, 11, 21, 17, 7, 31, 9, 21, 17, 17, 16, 17, 8, 29, 11, 30, 29, 2, 1, 33, 1, 26, 9, 1, 21, 6, 20, 15, 23, 11, 17, 39, 39, 33, 31, 17, 8, 9}

    {21, 43, 48, 49, 17, 39, 13, 36, 46, 31, 11, 31, 46, 30, 32, 50, 31, 20, 26, 39, 35, 31, 46, 47, 31, 35, 47, 11, 39, 1, 33, 49, 41, 29, 27, 31, 21, 30, 29, 34, 43, 40, 35, 41, 18, 10, 10}

    Returns: 0.02175548808646403

  41. {32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32}

    {32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32}

    {32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32}

    {32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32}

    Returns: 0.9999999999999799

  42. {23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23}

    {23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23}

    {43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43}

    {43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43}

    Returns: 0.0

  43. {1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    {1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 2, 2, 2, 1}

    {1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    {1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2}

    Returns: 0.6440329218106948

  44. {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    {2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2}

    {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1}

    {1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1}

    Returns: 0.6577909270216961

  45. {1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

    {2, 1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1}

    {1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1}

    {1, 1, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 1}

    Returns: 0.5727040816326536

  46. {1, 26, 5, 11, 9, 27, 15, 3, 1, 7, 1, 17, 30, 3, 22, 6, 5, 40, 23, 21, 5, 1, 15, 1, 28, 1, 33, 2, 1, 14, 19, 1, 36, 23, 1, 26, 9, 25, 27, 5, 35, 11, 36, 1, 25, 19, 21, 25, 17, 31}

    {37, 28, 13, 37, 34, 33, 29, 21, 33, 21, 17, 39, 36, 19, 31, 37, 21, 40, 29, 25, 9, 37, 33, 30, 31, 6, 37, 20, 5, 25, 31, 29, 39, 40, 1, 30, 30, 30, 33, 38, 36, 17, 39, 29, 33, 37, 26, 36, 39, 40}

    {15, 21, 17, 13, 21, 15, 34, 19, 21, 15, 27, 37, 11, 16, 31, 21, 31, 16, 23, 41, 31, 23, 15, 35, 13, 15, 26, 11, 33, 13, 11, 19, 35, 23, 18, 21, 35, 27, 25, 34, 41, 45, 16, 23, 20, 39, 29, 21, 39, 17}

    {19, 22, 35, 49, 24, 22, 34, 31, 41, 38, 39, 47, 33, 19, 35, 23, 48, 50, 31, 41, 46, 47, 38, 35, 35, 45, 49, 33, 49, 27, 47, 23, 49, 39, 19, 41, 37, 46, 31, 44, 43, 47, 27, 49, 41, 43, 39, 29, 47, 41}

    Returns: 0.02238533610274826

  47. {1, 13, 17, 1, 21, 1, 25, 5, 1, 35, 19, 5, 1, 1, 21, 1, 29, 1, 1, 3, 25, 8, 17, 22, 27, 31, 20, 1, 14, 17, 1, 1, 3, 1, 1, 1, 6, 1, 10, 1, 17, 7, 1, 16, 4, 4, 5, 8, 33, 1}

    {1, 16, 26, 13, 36, 31, 37, 33, 11, 37, 36, 29, 33, 18, 39, 36, 37, 33, 21, 23, 33, 26, 27, 37, 31, 36, 21, 29, 26, 33, 21, 40, 31, 26, 5, 8, 17, 29, 13, 31, 25, 27, 36, 17, 21, 31, 36, 10, 39, 37}

    {42, 12, 35, 11, 11, 11, 17, 11, 41, 23, 11, 26, 12, 11, 15, 11, 21, 31, 27, 18, 36, 11, 19, 16, 25, 15, 33, 27, 15, 11, 11, 21, 31, 35, 15, 33, 19, 31, 14, 19, 16, 35, 39, 31, 35, 11, 22, 11, 18, 19}

    {49, 47, 46, 33, 43, 26, 25, 19, 43, 46, 43, 48, 31, 15, 31, 33, 42, 35, 46, 40, 43, 39, 44, 27, 46, 46, 49, 31, 18, 19, 15, 24, 43, 38, 38, 48, 35, 41, 49, 38, 41, 43, 49, 31, 35, 12, 27, 27, 31, 41}

    Returns: 0.020504923450441373

  48. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}

    {50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50}

    {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}

    {50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50}

    Returns: 0.0200000000000089

  49. {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}

    {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}

    {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}

    {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}

    Returns: 0.99999999999995

  50. {5, 7, 7, 1, 6, 1, 1 }

    {8, 9, 7, 3, 9, 5, 3 }

    {9, 12, 10, 14, 50, 9, 10 }

    {9, 13, 50, 15, 50, 12, 11 }

    Returns: 0.014880952380952378

  51. {1, 6, 3, 1, 4, 3, 5, 1 }

    {7, 8, 5, 7, 9, 7, 9, 3 }

    {5, 1, 5, 3, 1, 2, 4, 1 }

    {9, 2, 7, 9, 4, 5, 4, 9 }

    Returns: 0.11562305130385474

  52. {1, 3, 5 }

    {7, 9, 9 }

    {2, 7, 3 }

    {9, 10, 4 }

    Returns: 0.10396825396825396

  53. {1, 5, 4, 3, 2, 5 }

    {4, 5, 5, 20, 48, 6 }

    {3, 14, 25, 36, 17, 1 }

    {5, 16, 25, 40, 17, 50 }

    Returns: 0.03869582348305762

  54. {1 }

    {1 }

    {1 }

    {1 }

    Returns: 1.0

  55. {1 }

    {3 }

    {1 }

    {1 }

    Returns: 0.3333333333333333

  56. {1, 2, 3 }

    {6, 7, 8 }

    {1, 2, 3 }

    {5, 6, 9 }

    Returns: 0.13597883597883603

  57. {1, 6, 3, 1, 4, 3, 5, 1, 1 }

    {7, 8, 5, 7, 9, 7, 9, 3, 2 }

    {5, 1, 5, 3, 1, 2, 4, 1, 3 }

    {9, 2, 7, 9, 4, 5, 4, 9, 4 }

    Returns: 0.11672881498278315

  58. {1, 6, 3, 1, 4, 3, 5, 1, 5, 7 }

    {7, 8, 5, 7, 9, 7, 9, 3, 6, 7 }

    {5, 1, 5, 3, 1, 2, 4, 1, 5, 5 }

    {9, 2, 7, 9, 4, 5, 4, 9, 5, 6 }

    Returns: 0.12470907029478458

  59. {2, 2, 2, 2, 2, 2 }

    {9, 9, 9, 9, 9, 9 }

    {1, 1, 1, 1, 1, 1 }

    {50, 50, 50, 50, 50, 50 }

    Returns: 0.020000000000000056

  60. {50 }

    {50 }

    {43 }

    {50 }

    Returns: 0.125

  61. {1 }

    {3 }

    {7 }

    {10 }

    Returns: 0.0

  62. {50 }

    {50 }

    {50 }

    {50 }

    Returns: 1.0

  63. {1, 5, 7, 8 }

    {7, 12, 15, 19 }

    {2, 4, 6, 7 }

    {10, 30, 40, 50 }

    Returns: 0.03400374564809092

  64. {3 }

    {5 }

    {2 }

    {6 }

    Returns: 0.2

This problem statement is the exclusive and proprietary property of TopCoder, Inc. Any unauthorized use or reproduction of this information without the prior written consent of TopCoder, Inc. is strictly prohibited. (c)2024, TopCoder, Inc. All rights reserved.
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